Question: Rewrite as a simplified fraction. ${0.51\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 516.6666...\\ 100x &= 51.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 465}$ ${x = \dfrac{465}{900}} $ ${x = \dfrac{31}{60}} $